Start with your rigged UDK character
Upload your character to UDK using the Content Browser
Set Package, Group and Name
Upload your character to Mixamo.com, select and customize your animation!
Set "Download w/Skin:" to "Skeleton Only"
Download the animation as FBX
Double click on your Skeletal Mesh to open the AnimSet Editor. In the AnimSet Editor go to File > New AnimSet
Assign the AnimSet to a Package, Group & Name. Go back to File and select "Import FBX Animation."
After uploading you'll see your animation in the Anim List.